It was more for an unknown individual than a known one, but extending it the way it has been is a very natural progression

So an example where you don’t know the individual would be

Somebody left their umbrella in the office. Could you please let them know where they can get it?

The more modern extended usage that people seem so up in arms about would be

Kate left their umbrella in the office. Could you please let them know where they can get it?